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A Story of Units®

GRADE 2 • MODULE 1
2
GRADE
Mathematics Curriculum
Table of Contents
Sums and Differences to 100
Module Overview.......................................................................................................... 2
Topic A: Foundations for Fluency with Sums and Differences Within 100 ................. 17
Topic B: Initiating Fluency with Addition and Subtraction Within 100 ....................... 45
End-of-Module Assessment and Rubric.................................................................... 110
Answer Key................................................................................................................ 117
Module 1: Sums and Differences to 100
A STORY OF UNITS
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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Module Overview 2 1
Grade 2 • Module 1
Sums and Differences to 100
OVERVIEW
Module 1 sets the foundation for students to master sums and differences to 20 (2.OA.2). Students
subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place
value understanding, properties of operations, and the relationship between addition and subtraction
(2.NBT.5). In Grade 1, students worked extensively with numbers to gain fluency with sums and differences
within 10 (1.OA.5) and became proficient in counting on (a Level 2 strategy). They also began to make easier
problems to add and subtract within 20 and 100 by making ten and taking from ten (Level 3 strategies)
(1.OA.6, 1.NBT.4–6).1
In Module 1, students advance from Grade 1’s subtraction of a multiple of ten to a new complexity,
subtracting single-digit numbers from both multiples of ten (e.g., 40 – 9) and from any two-digit number
within 100 (e.g., 41 – 9).
Topic A’s two lessons are devoted solely to the important practice of fluency, the first lesson working within
20 and the second extending the same fluencies to numbers within 100. Topic A reactivates students’
Kindergarten and Grade 1 learning as they energetically practice the following prerequisite skills for Level 3
decomposition and composition methods:
decompositions of numbers within ten2 (e.g., 0 + 7, 1 + 6, 2 + 5, and 3 + 4, all equal seven).
partners to ten3(e.g., 10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, and “I know 8 needs 2 to
make ten”).
tens plus sums4 (e.g., 10 + 9, 10 + 8).
1
See the Progression Documents “K, Counting and Cardinality” and “K-5, Operations and Algebraic Thinking” pp. 36 and 39,
respectively.
2
K.OA.3; 1.OA.6
3
K.OA.4
4
K.NBT.1; 1.NBT.2b
Level 2: Count on Level 3: Make an easier problem
40 – 9 = 31
/
30 10
10 – 9 = 1
30 + 1 = 31
41 – 9 = 32
/
31 10
10 – 9 = 1
31 + 1 = 32
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Module Overview 2 1
For example, students quickly remember make ten facts. They then immediately use those facts to solve
problems with larger numbers (e.g., “I know 8 needs 2 to make 10, so 58 needs 2 to make 6 tens or sixty!”).
Lessons 1 and 2 include Sprints that bring back automaticity with the tens plus sums, which are foundational
for adding within 100 and expanded form (e.g., “I know 10 + 8 = 18, so 40 + 8 = 48”).
Topic B takes Grade 1’s work to a new level of fluency as students make easier problems to add and subtract
within 100 by using the number system’s base ten structure. The topic begins with students using place value
understanding to solve problems by adding and subtracting like units (e.g., “I know 8 – 5 = 3, so 87 – 50 = 37
because 8 tens – 5 tens = 3 tens. I know 78 – 5, too, because 8 ones – 5 ones = 3 ones. I used the same easier
problem, 8 – 5 = 3, just with ones instead of tens!”). Students then practice making ten within 20 before
generalizing that strategy to numbers within 100 (e.g., “I know 9 + 6 = 15, so 79 + 6 = 85, and 89 + 6 = 95”).
The preceding lessons segue beautifully into the new concepts of Topic B, subtracting single-digit numbers
from two-digit numbers greater than 20. In Lesson 6, students use the familiar take from ten strategy to
subtract single-digit numbers from multiples of ten (e.g., 60 – 8, as shown below). In Lesson 7, students
practice taking from ten within 20 when there is the complexity of some ones in the total (e.g., 13 – 8, as
shown below). In Lesson 8, they then subtract single-digit numbers from 2-digit numbers within 100 when
there are also some ones (e.g., 63 – 8, as shown below).
These strategies deepen place value understandings in
preparation for Module 3 and the application of those
understandings to addition and subtraction in Modules 4 and 5.
Listen to how the language of make ten and take from ten is
foundational to the work of later modules:
Module 3: “I have 10 tens, so I can make a hundred. It’s just like I
can make a ten when I have 10 ones.”
Module 5: “When I solve 263 – 48, I take a ten from 6 tens to
make 5 tens and 13 ones. Now, I am ready to subtract in the ones
place” (pictured to the right).
Note that mastery of sums and differences within 100 is not to be expected in Module 1 but rather by Module
8. Because the amount of practice required by each student to achieve mastery prior to Grade 3 will vary, a
motivating, differentiated fluency program needs to be established in these first 2 weeks to set the tone for
the year.
Decompose and Subtract From Ten
63 – 8 = 55
/
53 10
10 – 8 = 2
53 + 2 = 55
60 – 8 = 52
/
50 10
10 – 8 = 2
50 + 2 = 52
13 – 8 = 5
/
3 10
10 – 8 = 2
3 + 2 = 5
Lesson 6 Lesson 8
Lesson 7
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Module Overview 2 1
In Grade 2 Module 1, Application Problems begin in Topic B. They contextualize learning as students apply
strategies to solving simple add to, take from, put together/take apart problem types using the Read-Draw-
Write, or RDW, process (2.OA.1). Application Problems may precede the Concept Development to act as the
lead-in, allowing students to discover through problem-solving the logic and usefulness of a strategy before it
is formally presented. Or, problems may follow the Concept Development so that students connect and
apply new learning to real-world situations. At the beginning of Grade 2, problem-solving may begin more as
a guided activity, with the goal being to move students to independent problem-solving, wherein they reason
through the relationships embedded within the problem and choose an appropriate strategy to solve (MP.5).
Notes on Pacing for Differentiation
It is not recommended to modify or omit any lessons in Module 1.
Focus Grade Level Standards
Represent and solve problems involving addition and subtraction.5
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem. (See CCLS Glossary, Table 1.)
Add and subtract within 20.6
2.OA.2 Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of
mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers.
6
From this point forward, fluency practice with addition and subtraction to 20 is part of the students’ ongoing experience.
6
From this point forward, fluency practice with addition and subtraction to 20 is part of the students’ ongoing experience.
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Module Overview 2 1
Use place value understanding and properties of operations to add and subtract.7
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction.
Foundational Standards
K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using
objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3
and 5 = 4 + 1).
K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number,
e.g., by using objects or drawings, and record the answer with a drawing or equation.
K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g.,
by using objects or drawings, and record each composition or decomposition by a drawing or
equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and
one, two, three, four, five, six, seven, eight, or nine ones.
1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use
strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing
a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship
between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known
equivalent 6 + 6 + 1 = 12 + 1 = 13).
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones—called a “ten.”
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six,
seven, eight, or nine ones.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a
two-digit number and a multiple of 10, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the reasoning used.
Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and
sometimes it is necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having
to count; explain the reasoning used.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive
or zero differences), using concrete models or drawings and strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
7
The balance of this cluster is addressed in Modules 4 and 5.
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Module Overview 2 1
Focus Standards for Mathematical Practice
MP.2 Reason abstractly and quantitatively. Students reason abstractly when they decontextualize
a word problem, representing a situation with a number sentence (e.g., Mark had a stick of 9
green linking cubes. His friend gave him 4 yellow linking cubes. How many linking cubes does
Mark have now?). In their solutions, students write 9 + 4 = 13. In so doing, they have
decontextualized the quantity from the situation. They then contextualize the solution when
they write a statement of the answer (e.g., “Mark has 13 linking cubes now”). They reason
that the 13 refers to the quantity, or number, of linking cubes.
MP.5 Use appropriate tools strategically. As students become more comfortable with tools and
make ten/take from ten strategies, they begin to make smart decisions about when these
tools might be useful to solve various problems.
MP.7 Look for and make use of structure. Students use the structure of the place value system to
add and subtract like units within 100 (e.g., “I know 8 – 5 = 3, so 87 – 50 = 37 because
8 tens – 5 tens = 3 tens. I know 78 – 5, too, because 8 ones – 5 ones = 3 ones. I used the
same easier problem, 8 – 5 = 3, just with ones instead of tens!”).
MP.8 Look for and express regularity in repeated reasoning. In order to use the make ten and take
from ten strategies efficiently, students practice completing a unit of ten during fluency in
many ways (e.g., the teacher flashes a ten-frame and students identify the missing part). This
skill is applied throughout the module. For example, students see the repeated reasoning of
taking from ten in Lessons 6, 7, and 8 to subtract single-digit numbers. Whether solving
30 – 9, 13 – 9, or 31 – 9, they take out the ten, subtract 9 from 10, and put together the parts
that are left (see image below).
30 – 9 = 21
/
20 10
10 – 9 = 1
20 + 1= 21
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Module Overview 2 1
Overview of Module Topics and Lesson Objectives
Standards Topics and Objectives Days
2.OA.2
K.OA.3
K.OA.4
K.NBT.1
1.NBT.2b
1.OA.5
1.OA.6
A Foundations for Fluency with Sums and Differences Within 100
Lesson 1: Practice making ten and adding to ten.
Lesson 2: Practice making the next ten and adding to a multiple of ten.
2
2.OA.1
2.OA.2
2.NBT.5
1.NBT.4
1.NBT.5
1.NBT.6
B Initiating Fluency with Addition and Subtraction Within 100
Lesson 3: Add and subtract like units.
Lesson 4: Make a ten to add within 20.
Lesson 6: Subtract single-digit numbers from multiples of 10 within 100.
Lesson 7: Take from ten within 20.
Lesson 8: Take from ten within 100.
6
End-of-Module Assessment: Topics A–B (assessment 1 day, return ½ day,
remediation or further applications ½ day)
2
Total Number of Instructional Days 10
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Module Overview 2 1
Terminology
New or Recently Introduced Terms
Make a ten (compose a unit of ten, e.g., 49 + 3 = 40 + 10 + 2)
Familiar Terms and Symbols8
Addend (one of the numbers being added)
A ten (a place value unit composed of 10 ones)
Count on (count up from one addend to the total)
Expression (e.g., 2 + 1, 13 – 6)
Like units (e.g., frogs and frogs, ones and ones, tens and tens)
Make ten and take from ten (e.g., 8 + 3 = 8 + 2 + 1 and 15 – 7 = 10 – 7 + 5 = 3 + 5)
Number sentence (e.g., 2 + 3 = 5, 7 = 9 – 2, 10 + 2 = 9 + 3)
Number bond (see image to the right)
One (a place value unit, 10 of which may be composed to make a ten)
Part (e.g., “What is the unknown part? 3 + ___ = 8”)
Partners to 10 (e.g., 10 and 0, 9 and 1, 8 and 2, 7 and 3,
6 and 4, 5 and 5)
Say Ten counting (see the chart to the right)
Ten plus facts (e.g., 10 + 3 = 13, 10 + 5 = 15, 10 + 8 = 18)
Total (e.g., for 3 + 4 = 7 or 7 – 4 = 3, seven is the whole, or
total)
Suggested Tools and Representations
100-bead Rekenrek
5-group column
Dice
Hide Zero cards (Lesson 2 Template 1)
Linking cubes
Number bond
Personal white boards
Place value chart
Quick ten (vertical line representing a unit of ten)
Ten-frame cards (Lesson 1 Fluency Template 1)
8
These are terms and symbols students have seen previously.
Number Bond
Hide Zero Cards
Ten-Frame Cards 5-Group
Column
Rekenrek
Quick Ten and Ones
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Module Overview 2 1
Suggested Methods of Instructional Delivery
Directions for Administration of Sprints
Sprints are designed to develop fluency. They should be fun, adrenaline-rich activities that intentionally build
energy and excitement. A fast pace is essential. During Sprint administration, teachers assume the role of
athletic coaches. A rousing routine fuels students’ motivation to do their personal best. Student recognition
of increasing success is critical, and so every improvement is celebrated.
One Sprint has two parts with closely related problems on each. Students complete the two parts of the
Sprint in quick succession with the goal of improving on the second part, even if only by one more.
With practice the following routine takes about 8 minutes.
Sprint A
Pass Sprint A out quickly, face down on student desks with instructions to not look at the problems until the
signal is given. (Some Sprints include words. If necessary, prior to starting the Sprint, quickly review the
words so that reading difficulty does not slow students down.)
T: You will have 60 seconds to do as many problems as you can.
T: I do not expect you to finish all of them. Just do as many as you can, your personal best. (If some
students are likely to finish before time is up, assign a number to count by on the back.)
T: Take your mark! Get set! THINK! (When you say THINK, students turn their papers over and work
furiously to finish as many problems as they can in 60 seconds. Time precisely.)
T: Stop! Circle the last problem you did. I will read just the answers. If you got it right, call out “Yes!”
If you made a mistake, circle it. Ready?
T: (Energetically, rapid-fire call the first answer.)
S: Yes!
T: (Energetically, rapid-fire call the second answer.)
S: Yes!
Repeat to the end of Sprint A or until no one has any more correct. If need be, read the count-by answers in
the same way the Sprint answers were read. Each number counted by on the back is considered a correct
answer.
T: Fantastic! Now, write the number you got correct at the top of your page. This is your personal goal
for Sprint B.
T: How many of you got 1 right? (All hands should go up.)
T: Keep your hand up until I say the number that is 1 more than the number you got right. So, if you
got 14 correct, when I say 15 your hand goes down. Ready?
T: (Quickly.) How many got 2 correct? 3? 4? 5? (Continue until all hands are down.)
Optional routine, depending on whether or not the class needs more practice with Sprint A:
T: I’ll give you one minute to do more problems on this half of the Sprint. If you finish, stand behind
your chair. (As students work, the person who scored highest on Sprint A could pass out Sprint B.)
T: Stop! I will read just the answers. If you got it right, call out “Yes!” If you made a mistake, circle it.
Ready? (Read the answers to the first half again as students stand.)
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Module Overview 2 1
Movement
To keep the energy and fun going, always do a stretch or a movement game in between Sprints A and B. For
example, the class might do jumping jacks while skip counting by 5 for about 1 minute. Feeling invigorated,
students take their seats for Sprint B, ready to make every effort to complete more problems this time.
Sprint B
Pass Sprint B out quickly, face down on student desks with instructions not to look at the problems until the
signal is given. (Repeat the procedure for Sprint A up through the show of hands for how many are right.)
T: Stand up if you got more correct on the second Sprint than on the first.
S: (Stand.)
T: Keep standing until I say the number that tells how many more you got right on Sprint B. So, if you
got 3 more right on Sprint B than you did on Sprint A, when I say 3, you sit down. Ready? (Call out
numbers starting with 1. Students sit as the number by which they improved is called. Celebrate the
students who improved most with a cheer.)
T: Well done! Now, take a moment to go back and correct your mistakes. Think about what patterns
you noticed in today’s Sprint.
T: How did the patterns help you get better at solving the problems?
T: Rally Robin your thinking with your partner for 1 minute. Go!
Rally Robin is a style of sharing in which partners trade information back and forth, one statement at a time
per person, for about 1 minute. This is an especially valuable part of the routine for students who benefit
from their friends’ support to identify patterns and try new strategies.
Students may take Sprints home.
RDW or Read, Draw, Write (a Number Sentence and a Statement)
Mathematicians and teachers suggest a simple process applicable to all grades:
1. Read.
2. Draw and label.
3. Write a number sentence.
4. Write a word sentence (statement).
The more students participate in reasoning through problems with a systematic approach, the more they
internalize those behaviors and thought processes.
What do I see?
Can I draw something?
What conclusions can I make from my drawing?
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Module Overview 2 1
Modeling with Interactive
Questioning
Guided Practice Independent Practice
The teacher models the whole
process with interactive
questioning, some choral
response, and talk such as “What
did Monique say, everyone?”
After completing the problem,
students might reflect with a
partner on the steps they used to
solve the problem. “Students,
think back on what we did to
solve this problem. What did we
do first?” Students might then
be given the same or a similar
problem to solve for homework.
Each student has a copy of the
question. Though guided by the
teacher, they work
independently at times and then
come together again. Timing is
important. Students might hear,
“You have 2 minutes to do your
drawing.” Or, “Put your pencils
down. Time to work together
again.” The Debrief might
include selecting different
student work to share.
The students are given a problem
to solve and possibly a
designated amount of time to
solve it. The teacher circulates,
supports, and thinks about which
student work to show to support
the mathematical objectives of
the lesson. When sharing
student work, students are
encouraged to think about the
work with questions such as,
“What do you notice about
Jeremy’s work?”
“What is the same about
Jeremy’s work and Sara’s work?”
Personal White Boards
Materials Needed for Personal White Boards
1 heavy duty, clear sheet protector
1 piece of stiff red tag board 11″ × 8 ¼″
1 piece of stiff white tag board 11″ × 8 ¼″
1 3″× 3″ piece of dark synthetic cloth for an eraser (e.g., felt)
1 low odor dry erase marker: fine point
Directions for Creating Personal White Boards
Cut the white and red tag to specifications. Slide into the sheet protector. Store the eraser on the red side.
Store markers in a separate container to avoid stretching the sheet protector.
Frequently Asked Questions About Personal White Boards
Why is one side red and one white?
The white side of the board is the “paper.” Students generally write on it and if working individually,
then turn the board over to signal to the teacher that they have completed their work. The teacher
then says, “Show me your boards,” when most of the class is ready.
What are some of the benefits of a personal white board?
The teacher can respond quickly to gaps in student understandings and skills. “Let’s do some of
these on our personal boards until we have more mastery.”
Student can erase quickly so that they do not have to suffer the evidence of their mistake.
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Module Overview 2 1
They are motivating. Students love both the drill and thrill capability and the chance to do story
problems with an engaging medium.
Checking work gives the teacher instant feedback about student understanding.
What is the benefit of this personal white board over a commercially purchased dry erase board?
It is much less expensive.
Templates such as place value charts, number bond mats, hundreds boards, and number lines can be
stored between the two pieces of tag for easy access and reuse.
Worksheets, story problems, and other problem sets can be done without marking the paper so that
students can work on the problems independently at another time.
Strips with story problems, number lines, and arrays can be inserted and still have a full piece of
paper on which to write.
The red versus white side distinction clarifies expectations. When working collaboratively, there is
no need to use the red side. When working independently, students know how to keep their work
private.
The sheet protector can be removed if necessary to project the work.
Scaffolds9
The scaffolds integrated into A Story of Units give alternatives for how students access information as well as
express and demonstrate their learning. Strategically placed margin notes are provided within each lesson
elaborating on the use of specific scaffolds at applicable times. They address many needs presented by
English language learners, students with disabilities, students performing above grade level, and students
performing below grade level. Many of the suggestions are organized by Universal Design for Learning (UDL)
principles and are applicable to more than one population. To read more about the approach to
differentiated instruction in A Story of Units, please refer to “How to Implement A Story of Units.”
9
Students with disabilities may require Braille, large print, audio, or special digital files. Please visit the website
www.p12.nysed.gov/specialed/aim for specific information on how to obtain student materials that satisfy the National Instructional
Materials Accessibility Standard (NIMAS) format.
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Module Overview 2 1
Preparing to Teach a Module
Preparation of lessons will be more effective and efficient if there has been an adequate analysis of the
module first. Each module in A Story of Units can be compared to a chapter in a book. How is the module
moving the plot, the mathematics, forward? What new learning is taking place? How are the topics and
objectives building on one another? The following is a suggested process for preparing to teach a module.
Step 1: Get a preview of the plot.
A: Read the Table of Contents. At a high level, what is the plot of the module? How does the story
develop across the topics?
B: Preview the module’s Exit Tickets10
to see the trajectory of the module’s mathematics and the nature
of the work students are expected to be able to do.
Note: When studying a PDF file, enter “Exit Ticket” into the search feature to navigate from one Exit
Ticket to the next.
Step 2: Dig into the details.
A: Dig into a careful reading of the Module Overview. While reading the narrative, liberally reference
the lessons and Topic Overviews to clarify the meaning of the text—the lessons demonstrate the
strategies, show how to use the models, clarify vocabulary, and build understanding of concepts.
Consider searching the video gallery on Eureka Math’s website to watch demonstrations of the use of
models and other teaching techniques.
B: Having thoroughly investigated the Module Overview, read through the chart entitled Overview of
Module Topics and Lesson Objectives to further discern the plot of the module. How do the topics
flow and tell a coherent story? How do the objectives move from simple to complex?
Step 3: Summarize the story.
Complete the Mid- and End-of-Module Assessments. Use the strategies and models presented in the
module to explain the thinking involved. Again, liberally reference the work done in the lessons to see
how students who are learning with the curriculum might respond.
10
A more in-depth preview can be done by searching the Problem Sets rather than the Exit Tickets. Furthermore, this same process
can be used to preview the coherence or flow of any component of the curriculum, such as Fluency Practice or Application Problems.
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Module Overview 2 1
Preparing to Teach a Lesson
A three-step process is suggested to prepare a lesson. It is understood that at times teachers may need to
make adjustments (customizations) to lessons to fit the time constraints and unique needs of their students.
The recommended planning process is outlined below. Note: The ladder of Step 2 is a metaphor for the
teaching sequence. The sequence can be seen not only at the macro level in the role that this lesson plays in
the overall story, but also at the lesson level, where each rung in the ladder represents the next step in
understanding or the next skill needed to reach the objective. To reach the objective, or the top of the
ladder, all students must be able to access the first rung and each successive rung.
Step 1: Discern the plot.
A: Briefly review the module’s Table of Contents, recalling the overall story of the module and analyzing
the role of this lesson in the module.
B: Read the Topic Overview related to the lesson, and then review the Problem Set and Exit Ticket of
each lesson in the topic.
C: Review the assessment following the topic, keeping in mind that assessments can be found midway
through the module and at the end of the module.
Step 2: Find the ladder.
A: Complete the lesson’s Problem Set.
B: Analyze and write notes on the new complexities of
each problem as well as the sequences and progressions
throughout problems (e.g., pictorial to abstract, smaller
to larger numbers, single- to multi-step problems). The
new complexities are the rungs of the ladder.
C: Anticipate where students might struggle, and write a
note about the potential cause of the struggle.
D: Answer the Student Debrief questions, always
anticipating how students will respond.
Step 3: Hone the lesson.
At times, the lesson and Problem Set are appropriate for all students and the day’s schedule. At others,
they may need customizing. If the decision is to customize based on either the needs of students or
scheduling constraints, a suggestion is to decide upon and designate “Must Do” and “Could Do”
problems.
A: Select “Must Do” problems from the Problem Set that meet the objective and provide a coherent
experience for students; reference the ladder. The expectation is that the majority of the class will
complete the “Must Do” problems within the allocated time. While choosing the “Must Do”
problems, keep in mind the need for a balance of calculations, various word problem types11
, and
work at both the pictorial and abstract levels.
11
See the Progression Documents “K, Counting and Cardinality” and “K−5, Operations and Algebraic Thinking” pp. 9 and 23,
respectively.
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Module Overview 2 1
B: “Must Do” problems might also include remedial work as necessary for the whole class, a small
group, or individual students. Depending on anticipated difficulties, those problems might take
different forms as shown in the chart below.
Anticipated Difficulty “Must Do” Remedial Problem Suggestion
The first problem of the Problem Set is
too challenging.
Write a short sequence of problems on the board that
provides a ladder to Problem 1. Direct the class or small
group to complete those first problems to empower them
to begin the Problem Set. Consider labeling these
problems “Zero Problems” since they are done prior to
Problem 1.
There is too big of a jump in complexity
between two problems.
Provide a problem or set of problems that creates a bridge
between the two problems. Label them with the number
of the problem they follow. For example, if the
challenging jump is between Problems 2 and 3, consider
labeling the bridging problems “Extra 2s.”
Students lack fluency or foundational
skills necessary for the lesson.
Before beginning the Problem Set, do a quick, engaging
fluency exercise, such as a Rapid White Board Exchange,
“Thrilling Drill,” or Sprint. Before beginning any fluency
activity for the first time, assess that students are poised
for success with the easiest problem in the set.
More work is needed at the concrete
or pictorial level.
Provide manipulatives or the opportunity to draw solution
strategies. Especially in Kindergarten, at times the
Problem Set or pencil and paper aspect might be
completely excluded, allowing students to simply work
with materials.
More work is needed at the abstract
level.
Hone the Problem Set to reduce the amount of drawing as
appropriate for certain students or the whole class.
C: “Could Do” problems are for students who work with greater fluency and understanding and can,
therefore, complete more work within a given time frame. Adjust the Exit Ticket and Homework to
reflect the “Must Do” problems or to address scheduling constraints.
D: At times, a particularly tricky problem might be designated as a “Challenge!” problem. This can be
motivating, especially for advanced students. Consider creating the opportunity for students to share
their “Challenge!” solutions with the class at a weekly session or on video.
E: Consider how to best use the vignettes of the Concept Development section of the lesson. Read
through the vignettes, and highlight selected parts to be included in the delivery of instruction so that
students can be independently successful on the assigned task.
F: Pay close attention to the questions chosen for the Student Debrief. Regularly ask students, “What
was the lesson’s learning goal today?” Help them articulate the goal.
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Module Overview 2 1
Assessment Summary
Type Administered Format Standards Addressed
End-of-Module
Assessment Task
After Topic C Constructed response with rubric 2.OA.1
2.OA.2
2.NBT.5
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2
GRADE
Topic A
Foundations for Fluency with Sums
and Differences Within 100
2.OA.2, K.OA.3, K.OA.4, K.NBT.1, 1.NBT.2b, 1.OA.5, 1.OA.6
Focus Standards: 2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know
from memory all sums of two one-digit numbers.
Instructional Days: 2
Coherence -Links from: G1–M2
G1–M4
G1–M6
Introduction to Place Value Through Addition and Subtraction Within 20
Place Value, Comparison, Addition and Subtraction to 40
Place Value, Comparison, Addition and Subtraction to 100
-Links to: G2–M4 Addition and Subtraction Within 200 with Word Problems to 100
G3–M2 Place Value and Problem Solving with Units of Measure
In this first topic of Grade 2, students set the stage for fluency with sums and differences within 100 (2.OA.2)
by focusing on three essential skills:
1. Knowing the decompositions of any number within 10 (K.OA.3, 1.OA.6),
2. Knowing partners to 10 (K.OA.4),
3. Knowing teen numbers as 10 + n (K.NBT.1, 1.NBT.2b).
Topic A energetically revisits this familiar ground from Kindergarten and
Grade 1 at a new pace.
In Lesson 1, targeted fluency work begins with ten-frame flashes where students
review ways to make and take from ten (e.g., 9 + 1 = 10, 10 – 9 = 1). Students
practice Say Ten counting on the Rekenrek (eleven or “ten 1,” pictured to the
right), and they become reacquainted with Sprints using a familiar 10 + n Sprint.
Finally, students decompose ten in different ways by rolling a die and recording
number bonds within 10 in “Target Practice.”
Lesson 2 follows a similar path as Lesson 1, with activities now extending to numbers within
100. Students review representations of two-digit numbers with quick tens and ones (see
image to the right) in preparation for upcoming work within the module. Students build
confidence and proficiency alternating between regular and Say Ten counting with the support
of Hide Zero cards and a 100-bead Rekenrek, saying “6 tens 4” for 64. The final fluency in
Lesson 2 focuses on making the next ten (e.g., 57 + 3 = 60), which is foundational to the
mastery of sums and differences to 100 (2.NBT.5).
Ten
Hide Zero
64
Topic A: Foundations for Fluency with Sums and Differences Within 100
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Topic A 2 1
The Application Problem and Concept Development are intentionally omitted from this topic to devote time
to reviewing foundational fluencies for sums and differences within 100. All the exercises herein should be
included in future fluency work as necessary so that students enter Grade 3 having memorized their single-
digit addition facts and demonstrated fluency with sums and differences within 100 (2.NBT.5).
A Teaching Sequence Toward Mastery of Foundations for Fluency with Sums and Differences Within 100
Objective 1: Practice making ten and adding to ten.
(Lesson 1
Objective 2: Practice making the next ten and adding to a multiple of ten.
(Lesson 2
Topic A: Foundations for Fluency with Sums and Differences Within 100
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Lesson 1 2 1
NOTES ON
TOPIC A’S LESSON
STRUCTURE:
Grade 2 students spend much of the
year adding and subtracting.
Topic A’s lessons are a review of many
of the fluency activities and
experiences students know well from
Grade 1. The purpose of the two days
is to joyfully quicken the pace of
Grade 1 work, establish new class
routines, and remember foundational
skills necessary for success with fluency
with sums and differences within 100,
a Grade 2 fluency goal. The Concept
Development lessons begin in Topic B.
Lesson 1
Objective: Practice making ten and adding to ten.
Suggested Lesson Structure
Fluency Practice (47 minutes)
Student Debrief (13 minutes)
Total Time (60 minutes)
Fluency Practice (47minutes)
Ten-Frame Flash 2.OA.2 (5 minutes)
Happy Counting the Say Ten Way 2.OA.2 (6 minutes)
Sprint: Add a Ten and Some Ones 2.OA.2 (18 minutes)
Target Practice: Within 10 2.OA.2 (10 minutes)
Pairs to Ten with Number Bonds 2.OA.2 (8 minutes)
Ten-Frame Flash (5 minutes)
Materials: (T) Ten-frame cards (Fluency Template 1), 5-group
column cards (Fluency Template 2)
Note: By alternating between ten-frame and 5-groups column cards, students develop flexible perception of
numbers 6–10 in two parts, with one part as 5. This activity practices the core fluency objective from Grade
1, adding and subtracting within 10.
The teacher flashes a ten-frame card for 2–3 seconds and guides students to respond on a signal. Students
then generate a number sentence to get to 10.
T: (Flash the 9 ten-frame card. Give the signal.)
S: 9.
T: How much does 9 need to make 10?
S: 1.
T: Say the addition number sentence to make 10, starting with 9.
S: 9 + 1 = 10.
T: (Continue to show the 9 card.) Tell me a related subtraction sentence starting with 10.
S: 10 – 1 = 9. 10 – 9= 1.
Continue the process, using both ten-frame cards and 5-group column cards in the following suggested
sequence: 8, 2, 5, 7, 3, 6, 4, 10, and 0.
MP.8
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Lesson 1 2 1
Happy Counting the Say Ten Way (6 minutes)
Materials: (T) 100-bead Rekenrek (or Slavonic Abacus)
Note: East Asian or Say Ten counting (e.g., 13 is said ten 3) matches the base ten structure of numbers. In
contrast, the English language says the ten after the ones (e.g., four-teen). This makes fourteen easily
confused with forty. Since Kindergarten, in A Story of Units, students have been counting the Say Ten way, a
practice substantiated by research1
.
Part 1: Happy Counting on the Rekenrek
T: Let’s count the Say Ten way.
T: (Show 10 beads. Move one at a time as students count.)
T: Ten 1. Say it with me. (See image to the right.)
S: Ten 1.
T: (Move the beads and have students count ten 2, ten 3, ten 4,
ten 5, ten 6, ten 7, ten 8, ten 9, 2 tens.)
T: (Take one bead away.) Tell me the number the Say Ten way.
S: Ten 9.
Continue to count up and down within 20 as students call out the number the Say Ten way. As students
demonstrate proficiency, consider alternating between the Say Ten way and the regular way (e.g., eleven,
twelve, thirteen, fourteen, fifteen, sixteen, change to Say Ten counting and go down, ten 5, ten 4).
Part 2: Happy Counting
When Happy Counting, make the motions emphatic so counting is sharp and crisp. As students improve, up
the challenge by increasing the speed and the number of direction changes or by using higher numbers. Be
careful not to mouth the numbers!
T: Now, let’s do some Happy Counting without the beads. Watch my thumb to know whether to count
up or down. A thumb in the middle means pause. (Show signals as you explain.)
T: Let’s count by ones starting at ten 3. Ready? (Rhythmically point up or down depending on if you
want students to count up or count down.)
S: Ten 3, ten 4, ten 5, ten 6, (pause) ten 5, ten 4, (pause) ten 5, ten 6, ten 7, ten 8, (pause) ten 7,
(pause) ten 8, ten 9, 2 tens.
1
Progressions for the Common Core State Standards: “K-5, Numbers and Operations in Base Ten” (pp. 5)
Ten 1
Ten 3 ten 4 ten 5 ten 6 pause ten 5 ten 4 pause ten 5 ten 6 ten 7 etc.
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Lesson 1 2 1
NOTES ON
MULTIPLE MEANS
OF ACTION AND
EXPRESSION:
For Sprints, a fast pace is essential to
build energy and excitement. To
support students who do not excel
under pressure, give them the chance
to practice the Sprint at home the
night before it is administered.
To maintain a high level of energy and
enthusiasm, always do a stretch or
movement game in between Sprint A
and Sprint B. For example, do jumping
jacks while skip-counting by fives.
NOTES ON
MULTIPLE MEANS
OF ACTION AND
REPRESENTATION:
For students who have not yet
mastered their pairs to ten, use
fingers as models. Have students
show the larger addend on their
fingers and encourage them to look
at their tucked fingers to determine
the partner to make ten.
Part 3: Say Ten as Ten Plus Facts
To segue to the upcoming Sprint, students say addition sentences for teen numbers when one addend is 10.
Alternate between the regular way and the Say Ten way.
T: If I say ten 2, you say 10 + 2 = 12.
T: What do you say if I say thirteen?
S: 10 + 3 = 13.
T: Yes! You guessed the pattern. Here’s another. Ten 5.
S: 10 + 5 = 15.
T: Fourteen.
S: 10 + 4 = 14.
Use the following suggested sequence: ten 6, seventeen,
eighteen, ten 5, eleven, ten 8, ten 1, etc.
Sprint: Add a Ten and Some Ones (18 minutes)
Materials: (S) Add Ten and Some Ones Sprint
Note: See the Suggested Methods of Instructional Delivery in
the Module Overview for clear instructions on administering
Sprints. This Sprint brings automaticity back with the ten plus
sums, which are foundational for the make a ten strategy and
expanded form.
Target Practice: Within 10 (10 minutes)
Materials: (S) Per set of partners: personal white board, target practice (Fluency Template 3), 1 numeral die
Note: Decomposition of single-digit numbers and 10 is a foundational skill for fluency with sums and
differences to 20.
Assign Partner A and Partner B. Students write the target
number, 10, in the circle at the top right of the target practice
template.
Directions:
Partner A rolls the die.
Partner A writes the number rolled in one part of the
first number bond.
Partner B makes a bull’s eye by writing the missing part
that is needed to make ten.
Adjust the target number as appropriate for each pair of
students, focusing on totals of 6, 7, 8, 9, and 10.
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Lesson 1 2 1
NOTES ON
STUDENT DEBRIEF:
To close the majority of lessons,
invite students to figure out the
math goal. As the year progresses,
they will come to anticipate this
question, and responses will get
increasingly mathematical, precise,
and insightful. By engaging in the
metacognitive exercise of
articulating the goal, students take
another step toward owning their
learning. When possible, also ask
students, “How would you teach
this? Who would you teach it to?”
Pairs to Ten with Number Bonds (8 minutes)
Materials: (S) Personal white board
Note: This is a foundational skill for mastery of sums and differences to 20.
T: I’ll show a number bond, and you tell me the missing part to make 10.
T: (Draw the bond shown to the right.)
S: 5.
T: (Erase the 5 and write 8.)
S: 2.
Continue with the following suggested sequence: 9, 7, 3, 6, 4, 1, 10, and 0.
T: With your partner, take turns saying pairs to make 10. Partner A, you will go first for now.
After about 30 seconds, have partners switch roles.
Lesson Objective: Practice making ten and adding to ten.
The Student Debrief is intended to invite reflection and active
processing of the total lesson experience.
Guide students in a conversation to debrief today’s lesson.
Any combination of the questions below may be used to lead
the discussion.
What math work did we do today that you remember
from last year?
What do you hope to get better at in math this year?
Do you have a favorite math fact and why?
Can you figure out the math goal of today’s lesson?
What name would you give this lesson?
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read aloud to the students.
10
5
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Lesson 1 Sprint 2 1
Name Date
Add a Ten and Some Ones
1. 10 + 1 = ____ 16. 3 + 10 = ____
2. 10 + 2 = ____ 17. 4 + 10 = ____
3. 10 + 4 = ____ 18. 1 + 10 = ____
4. 10 + 3 = ____ 19. 2 + 10 = ____
5. 10 + 5 = ____ 20. 5 + 10 = ____
6. 10 + 6 = ____ 21. ____ = 10 + 5
7. ____ = 10 + 1 22. ____ = 10 + 8
8. ____ = 10 + 4 23. ____ = 10 + 9
9. ____ = 10 + 3 24. ____ = 10 + 6
10. ____ = 10 + 5 25. ____ = 10 + 7
11. ____ = 10 + 2 26. 16 = ____ + 6
12. 10 + 6 = ____ 27. 8 + ____ = 18
13. 10 + 9 = ____ 28. ____ + 10 = 17
14. 10 + 7 = ____ 29. 19 = ____ + 10
15. 10 + 8 = ____ 30. 18 = 8 + ____
Number Correct:
A
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Lesson 1 Sprint 2 1
Name Date
Add a Ten and Some Ones
1. 10 + 5 = ____ 16. 4 + 10 = ____
2. 10 + 4 = ____ 17. 3 + 10 = ____
3. 10 + 3 = ____ 18. 2 + 10 = ____
4. 10 + 2 = ____ 19. 1 + 10 = ____
5. 10 + 1 = ____ 20. 3 + 10 = ____
6. 10 + 5 = ____ 21. ____ = 10 + 6
7. ____ = 10 + 4 22. ____ = 10 + 9
8. ____ = 10 + 2 23. ____ = 10 + 5
9. ____ = 10 + 1 24. ____ = 10 + 7
10. ____ = 10 + 3 25. ____ = 10 + 8
11. ____ = 10 + 4 26. 17 = ____ + 7
12. 10 + 6 = ____ 27. 3 + ____ = 13
13. 10 + 7 = ____ 28. ____ + 10 = 16
14. 10 + 9 = ____ 29. 18 = ____ + 10
15. 10 + 8 = ____ 30. 17 = 7 + ____
Improvement: Number Correct:
B
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Lesson 1 Exit Ticket 2 1
Name Date
1. Add or subtract. Complete the number bond to match.
a. 9 + 1 = ____ b. 4 + 6 = ____
1 + 9 = ____ 6 + 4 = ____
10 – 1 = ____ 10 – 6 = ____
10 – 9 = ____ 10 – 4 = ____
2. Solve.
a. 10 + 5 = ____ b. 13 = 10 + ____ c. 10 + 8 = ____
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Name Date
1. Add or subtract. Complete the number bond for each set.
9 + 1 = ____ 8 + 2 = ____
1 + 9 = ____ 2 + 8 = ____
10 – 1 = ____ 10 – 2 = ____
10 – 9 = ____ 10 – 8 = ____
2. Solve. Draw a number bond for each set.
6 + 4 = ____ 3 + 7 = ____
4 + 6 = ____ 7 + 3 = ____
10 – 4 = ____ 10 – 7 = ____
10 – 6 = ____ 10 – 3 = ____
3. Solve.
10 = 7 + ____ 10 = ____ + 8
10 = 3 + ____ 10 = ____ + 4
10 = 5 + ____ 10 = ____ + 6
10 = 2 + ____ 10 = ____ + 1
10
1 9
Lesson 1 Homework 2 1
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Lesson 1 Fluency Template 1 2 1
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ten-frame cards
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ten-frame cards
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ten-frame cards
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5-group column cards
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Lesson 1 Fluency Template 3 2
Target Practice
Choose a target number, and write it in the middle of the circle on the top of the page.
Roll a die. Write the number rolled in the circle at the end of one of the arrows. Then,
make a bull’s eye by writing the number needed to make your target in the other
circle.
target practice
Target Number:
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Lesson 2 2 1
Lesson 2
Objective: Practice making the next ten and adding to a multiple of ten.
The Value of Tens and Ones 2.OA.2 (4 minutes)
Happy Counting the Say Ten Way 2.OA.2 (10 minutes)
Sprint: Add Tens and Ones 2.OA.2 (18 minutes)
Target Practice: Within 10 2.OA.2 (10 minutes)
Make the Next Ten 2.OA.2 (8 minutes)
The Value of Tens and Ones (4 minutes)
Note: This activity reviews representing two-digit numbers with quick tens and ones in preparation for
upcoming work within the module.
T: Tell me the total value of my tens and ones when I give the signal.
(Draw 1 quick ten and 7 ones.)
S: 17.
T: The Say Ten way?
S: 1 ten 7.
T: Say the addition sentence to add the ten and ones.
S: 10 + 7 = 17.
T: (Draw 2 tens and 2 ones. Give the signal.) Tell me the total value.
S: 22.
T: The Say Ten way?
S: 2 tens 2.
T: Say the addition sentence starting with the larger
number.
S: 20 + 2 = 22.
Continue the process using the following possible sequence:
29, 32, 38, 61, 64, 72, 81, 99, and 100.
22
64
38
17
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Lesson 2 2 1
Happy Counting the Say Ten Way (10 minutes)
Materials: (T) 100-bead Rekenrek, Hide Zero cards (Fluency Template)
Note: Repeating a similar fluency activity two days in a row gives students confidence and allows them
to build proficiency.
Part 1: Say Ten Counting with the Rekenrek and Hide Zero Cards
T: (Show 11 with the Hide Zero cards. Pull them apart to show the 10 and the 1. Repeat silently with
15 and 19.)
T: (Show 12 with Hide Zero cards.) Say the number the regular way?
S: 12.
T: (Pull cards apart.) The Say Ten way?
S: Ten 2.
T: (Show 13.) The Say Ten way?
S: Ten 3.
T: The regular way?
S: 13.
T: Let’s Say Ten count starting from 15 using the Rekenrek.
(To show 15, pull to the left a row of ten and a second row of five.)
T: Count the beads on the left the Say Ten way. (Show 15 beads.)
S: Ten 5, ten 6, ten 7, ten 8, ten 9.
T: 2 tens (show two rows of ten beads pulled to the left), and the pattern begins again.
S: 2 tens 1, 2 tens 2, 2 tens 3, 2 tens 4, 2 tens 5.
T: Let’s start with a new number. (Move beads to show 47.)
T: How much do I have?
S: 47.
T: What is 47 the Say Ten way? (Pictured to the right.)
S: 4 tens 7.
For about 2 minutes, students count up and down within 100. Each 20
to 30 seconds, begin a new counting sequence starting from a larger
decade. While moving up and down, cross over tens frequently (e.g.,
38, 39, 40, 41, 40, 39 or 83, 82, 81, 80, 79, 78, 79, 80, 81) as this is
more challenging, especially counting down.
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Lesson 2 2 1
NOTES ON
MULTIPLE MEANS
OF ENGAGEMENT:
For students who have mastered
partners within 10, assign numbers
within 20 as the target number.
NOTES ON
MULTIPLE MEANS
OF ACTION AND
EXPRESSION:
For students who are performing
significantly below grade level and
were unable to work past the first
10 questions in Lesson 1, perhaps let
them do “Add a Ten and Some
Ones” again today, this time with
drawings or materials.
Part 2: Happy Counting
T: Follow my hand as we Happy Count. Watch my thumb.
T: Let’s start at 2 tens 8. (Stop before students start to lose enthusiasm, after about 1 minute.)
T: Excellent! Try it with your partner. Partner A, you are the teacher today. I’ll give you 30 seconds.
To segue to the Sprint in the following activity, ask students to share the number sentences for the following
numbers.
T: Let’s share number sentences that break apart two-digit numbers into tens and ones. (Show 28 on
the Rekenrek and with Hide Zero cards.) I say 2 tens 8, and you say 20 + 8 = 28. (Break apart Hide
Zero cards to show 20 and 8.)
T: 2 tens 8.
S: 20 + 8 = 28.
T: (Write 20 + 8 = 28.)
T: 5 tens 3.
S: 50 + 3 = 53.
T: (Write 50 + 3 = 53.)
Use the following suggested sequence: 36, 19, 58, 77, 89, 90.
Sprint: Add Tens and Ones (18 minutes)
Materials: (S) Add Tens and Some Ones Sprint
Note: This Sprint brings automaticity back with the tens plus
sums, which are foundational for adding within 100 and
expanded form.
Target Practice: Within 10 (10 minutes)
Materials: (S) Per set of partners: personal white board, target practice (Lesson 1 Fluency Template 3), 1
numeral die
Note: Decomposition of single-digit numbers and 10 is a foundational skill for fluency with sums and
differences to 20.
Assign Partner A and Partner B. Students write their choice of
target number in the circle at the top right of the Target Practice
template.
Partner A rolls the die.
Partner A writes the number rolled in the circle at the
end of one of the arrows.
Partner B makes a bull’s eye by writing the number in
the other circle that is needed to make the target.
Adjust the target number as appropriate for each pair of students, focusing on totals of 6, 7, 8, 9, and 10. If
the pair demonstrates fluency, challenge them to move into teen numbers!
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Lesson 2 2 1
Make the Next Ten (8 minutes)
Note: This is a foundational skill for mastery of sums and differences to 20. If students do not know their
partners to 10, do not advance to making multiples of ten.
T: I’ll say a number, and you tell me what it needs to make the next 10.
T: 8. Get ready.
S: 2.
T: 28.
S: 2.
T: 58.
S: 2.
Continue the process using the following possible sequence: 7, 27, 67, 87.
T: With your partner, take turns saying pairs to make 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100. It’s your
choice. Partner A, you will go first for now.
After about 30 seconds, have partners switch roles. Keep it fun and joyful!
Lesson Objective: Practice making the next ten and adding to a multiple of ten.
The Student Debrief is intended to invite reflection and active processing of the total lesson experience.
Guide students in a conversation to debrief today’s lesson.
Any combination of the questions below may be used to lead the discussion.
How does knowing 10 + 3 help us with 50 + 3?
How does knowing that 8 needs 2 to make ten help us know how to get from 28 to the next ten?
How are Hide Zero cards and the Rekenrek similar? How are they different?
What learning today did you remember from last year?
Can you figure out the math goal of today’s lesson? What name would you give this lesson?
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read aloud to the students.
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Name Date
Add Tens and Ones
1. 10 + 3 =____ 16. 10 + ____ = 13
2. 20 + 2 =____ 17. 40 + ____ = 42
3. 30 + 4 =____ 18. 60 + ____ = 61
4. 50 + 3 =____ 19. 70 + ____ = 75
5. 20 + 5 =____ 20. 80 + ____ = 83
6. 50 + 5 =____ 21. 60 + 9 =____
7. ____ = 40 + 1 22. 80 + 9 =____
8. ____ = 20 + 4 23. 80 + ___ = 86
9. ____ = 20 + 3 24. 90 + ___ = 97
10. ____ = 30 + 5 25. ___ + 6 = 76
11. ____ = 40 + 5 26. ___ + 6 = 86
12. 30 + 6 =____ 27. 86 = ___ + 6
13. 20 + 9 =____ 28. ___ + 60 = 67
14. 40 + 7 =____ 29. 95 = ___ + 90
15. 50 + 8 =____ 30. 97 = 7 + ___
Number Correct:
A
Lesson 2 Sprint 2 1
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Name Date
Add Tens and Ones
1. 10 + 2 =____ 16. 10 + ____ = 12
2. 20 + 3 =____ 17. 40 + ____ = 42
3. 30 + 4 =____ 18. 60 + ____ = 61
4. 50 + 4 =____ 19. 70 + ____ = 75
5. 40 + 5 =____ 20. 80 + ____ = 83
6. 50 + 1 =____ 21. 70 + 8 =____
7. ____ = 50 + 1 22. 80 + 8 =____
8. ____ = 20 + 4 23. 70 + ___ = 76
9. ____ = 20 + 2 24. 90 + ___ = 99
10. ____ = 30 + 5 25. ___ + 8 = 78
11. ____ = 40 + 3 26. ___ + 6 = 96
12. 30 + 7 =____ 27. 86 = ___ + 6
13. 20 + 8 =____ 28. ___ + 60 = 67
14. 40 + 9 =____ 29. 95 = ___ + 90
15. 50 + 6 =____ 30. 97 = 7 + ___
Improvement: Number Correct:
B
Lesson 2 Sprint 2 1
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Name Date
Solve.
1. 2.
a. 10 + 3 = ____
b. 30 + 4 = ____
c. 60 + 5 = ____
d. 90 + 1 = ____
a. ____ = 10 + 7
b. ____ = 20 + 9
c. ____ = 70 + 6
d. ____ = 90 + 8
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Name Date
1. Add or subtract. Draw a number bond for (b).
a. 6 + 2 = ____ b. ____ = 3 + 5
2 + 6 = ____ ____ = 5 + 3
8 – 2 = ____ ____ = 8 – 3
8 – 6 = ____ ____ = 8 – 5
2. Solve.
20 + 4 = ____ ____ = 20 + 9
40 + 3 = ____ ____ = 40 + 8
70 + 2 = ____ ____ = 50 + 6
80 + 5 = ____ ____ = 90 + 7
3. Solve.
14 = 10 + ____ 19 = ____ + 9
23 = 20 + ____ 29 = ____ + 9
71 = 70 + ____ 78 = ____ + 8
82 = 80 + ____ 87 = ____ + 7
8
6 2
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Name Date
Number Bond Dash
Do as many as you can in 90 seconds. Write the number of bonds you finished here:
1. 2. 3. 4. 5.
6. 7. 8. 9. 10.
11. 12. 13. 14. 15.
16. 17. 18. 19. 20.
9
9
8
9
7
9
8
9
7
9
9
9
6
9
7
9
6
9
1
9
8
9
1
9
7
9
2
9
6
9
5
9
6
9
7
9
2
9
3
5
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Hide Zero cards
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Hide Zero cards
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2
GRADE
Topic B
Initiating Fluency with Addition and
Subtraction Within 100
2.OA.1, 2.OA.2, 2.NBT.5, 1.NBT.4, 1.NBT.5, 1.NBT.6
Focus Standards: 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems
involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using drawings and equations with a
symbol for the unknown number to represent the problem.
2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know
from memory all sums of two one-digit numbers.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction.
Instructional Days: 6
Coherence -Links from: G1–M2 Introduction to Place Value Through Addition and Subtraction Within 20
G1–M4 Place Value, Comparison, Addition and Subtraction to 40
G1–M6 Place Value, Comparison, Addition and Subtraction to 100
-Links to: G2–M4 Addition and Subtraction Within 200 with Word Problems to 100
G3–M2 Place Value and Problem Solving with Units of Measure
Now that students have sharpened their skills, they are ready to solve problems by decomposing and
composing units. Lessons 3, 4, 5, and 7 revisit Grade 1 learning at a new pace and without a heavy reliance
upon concrete and pictorial models while simultaneously preparing students for the new learning of Lessons
6 and 8, subtracting single-digit numbers from two-digit numbers within 100.
In Lesson 3, students use their understanding of place value to add and subtract like units, by decomposing
addends into tens and ones. For example, students apply their knowledge that 7 – 2 = 5 to solve 47 – 2
(7 ones – 2 ones = 5 ones) and 73 – 20 (7 tens – 2 tens = 5 tens).
Topic B: Initiating Fluency with Addition and Subtraction Within 100
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In Lesson 4, students use the Grade 1 make ten strategy. For example, to add 9 + 4
(pictured to the right), students decompose 4 as 1 and 3 in order to complete a unit of
ten (9 + 1) and then add, or compose, the ten with the remaining ones (10 + 3). They
then apply the same understanding to make the next ten (pictured below) in Lesson 5.
In Lesson 6, students advance their Grade 1 take from ten strategy to subtract single-digit numbers from
multiples of 10. For example, 30 – 9 is solved by decomposing 30 as 20 and 10, taking from ten (10 – 9), and
composing the parts that are left (20 + 1).
In Lesson 7, students practice the Grade 1 take from ten strategy within 20. Students repeat the same
reasoning from Lesson 6. For example, 11 – 9 is solved by decomposing 11 as 1 and 10, taking from ten (10 –
9), and composing the parts that are left (1 + 1).
30 – 9 = 21
/
20 10
10 – 9 = 1
20 + 1= 21
11 – 9 = 2
/
1 10
10 – 9 = 1
1 + 1 = 2
Topic B 2 1
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Topic B culminates with Lesson 8, where students, as in Lesson
6, extend the take from ten strategy to numbers within 100
(2.NBT.5). For example, to solve 41 – 9, students decompose 41
as 31 and 10, take from ten (10 – 9), and add the parts that are
left (31 + 1). Notice how the student talking to the right has
now generalized the process from the specific problem.
Making a ten and taking from ten are strategies that lay the
foundation for understanding place value and the base ten system.
These Level 3 composition and decomposition methods powerfully
pave the way for composing units and decomposing units of ten and
a hundred when using the addition and subtraction algorithms in
Modules 4 and 5. Furthermore, they exemplify Mathematical
Practice 8, as students look for the opportunity to repeat patterns of
reasoning both when calculating and in the context of word
problems.
In Topic B, Application Problems contextualize learning as students apply strategies to problem solving using
the RDW process. Students solve add to, take from, put together/take apart problem types with unknowns in
different positions (2.OA.1). They demonstrate their understanding of the situation by representing it with a
drawing, number sentence, and statement.
Mary buys 30 stickers. She puts 7 in her friend’s backpack. How many stickers does Mary have left?
Many students will enter Grade 2 drawing simple circles or 5-groups to reason through and represent a given
situation. Encourage sense making, and accept all reasonable drawings. Drawing a tape diagram to
accurately represent story situations comes with time and practice.
Topic B 2 1
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A Teaching Sequence Toward Mastery of Initiating Fluency with Addition and Subtraction Within 100
Objective 1: Add and subtract like units.
(Lesson 3)
Objective 2: Make a ten to add within 20.
(Lesson 4)
Objective 3: Make a ten to add within 100.
(Lesson 5)
Objective 4: Subtract single-digit numbers from multiples of 10 within 100.
(Lesson 6)
Objective 5: Take from ten within 20.
(Lesson 7)
Objective 6: Take from ten within 100.
(Lesson )
Topic B 2 1
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Lesson 3 2 1
NOTES ON
MULTIPLE MEANS
OF REPRESENTATION:
Consider demonstrating on the 100-
bead Rekenrek for students who would
benefit from a concrete model of the
problems.
Lesson 3
Objective: Add and subtract like units.
Concept Development (20 minutes)
Application Problem (15 minutes)
Sprint: Related Facts 2.OA.2 (15 minutes)
Sprint: Related Facts (15 minutes)
Materials: (S) Related Facts Sprint
Note: Students use their fluency with easier problems to solve more complex addition and subtraction
problems within 100. Also, as students get better with the Sprint routine, the time allotted for the Sprint
continues to decrease.
Part 1: Add and subtract like units, ones, to solve problems within 100 (e.g., 5 + 2, 45 + 2, 7 – 2, 47 – 2).
T: What did you notice about today’s Sprint?
S: I noticed a pattern. I saw 3 + 1 in the first 3 problems.
3 + 1 = 4. So, I also know that 13 + 1 = 14 and
23 + 1 = 24. I kept adding the same ones together
in the first 3 problems, 3 + 1 = 4. But the tens changed.
T: Yes! Today’s Sprint was filled with patterns. You can
use easier facts like 3 + 1 to solve other problems like
13 + 1 and 23 + 1.
T: Turn and talk to your partner about other patterns you
see in the Sprint.
S: (Identify sequences of problems.)
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Lesson 3 2 1
T: (Draw an image of 5 circles and 2 Xs as shown to the right.)
Say addition and subtraction sentences this drawing
represents.
S: 5 + 2 = 7. 2 + 5 = 7. 7 – 5 = 2. 7 – 2 = 5.
T: Just like in our Sprint today, we can use problems like
5 + 2 = 7 or 7 – 2 = 5 to solve other problems. (Write
5 + 2 = 7 and 7 – 2 = 5. Add 4 quick tens to the drawing.)
T: 45 + 2 is…?
S: 47.
T: (Write 45 + 2 = 47.)
T: 47 – 2 is…?
S: 45.
T: (Write 47 – 2 = 45.)
T: What easier problem did you use to add and to subtract?
S: 5 + 2 = 7. 7 – 2 = 5.
T: (Add 2 more quick tens to the drawing.) 67 – 2 is…?
S: 65.
T: (Add subtraction number sentences to the growing list.) What easier problem did we still use to
subtract the ones?
S: 7 – 2 = 5.
T: Tell me the number sentence in unit form.
S: 7 ones – 2 ones = 5 ones.
T: We didn’t have to do anything to the tens except remember to put them together with the 5 ones!
Part 2: Add and subtract like units, tens, to solve problems within 100 (e.g., 51 + 20, 54 + 20, 71 – 20, 74 – 20).
T: (Write 51 + 20 on the board.) 51 + 20 is…?
S: 71.
T: How did you know?
S: I added 20 to 50 to get 70 and then added 1. I drew
a quick ten drawing. I added 2 more tens to my 5 tens.
That gave me 7 tens and 1 one.
T: (Write the number bond to break apart 51 into 50 and
1.) How many tens are in 51?
S: 5 tens.
T: How many tens were we adding to 51?
S: 2 tens.
NOTES ON
MULTIPLE MEANS
OF ENGAGMENT:
Have students who struggle to see the
like units draw quick tens to represent
the problems. As soon as possible,
have them visualize the quick tens to
prevent overdependence on drawing.
“Pretend you drew quick tens. How
many do you see? How many do you
subtract? How many are left?”
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Lesson 3 2 1
T: What easier problem did you use to help you solve 51 and 20? Talk to your partner.
S: 5 + 2 = 7. 5 tens + 2 tens = 7 tens. 50 + 20 = 70.
Repeat the same reasoning with 54 + 20 and 58 + 20.
T: Compare 54 + 2 to 54 + 20. Talk to your partner.
S: We start with the same number in both problems.
In one problem, we add 2 ones. In the other
problem, we add 2 tens. Adding 2 ones is not the
same as adding 2 tens. 56 is much less than 74.
In one problem, we leave the ones alone, and in the
other problem, we leave the tens alone.
T: (Write 71 – 20.) Break apart 71 as tens and ones.
S: 70 and 1.
T: (Write the number bond for 71.) What is 71 – 20?
S: 51.
T: How did you know?
S: 7 tens – 2 tens = 5 tens. I took tens from tens. 70 – 20 = 50. Then I added 1. I used an easier
problem. I know 7 – 2 = 5, so 70 – 20 = 50.
Repeat the same reasoning with 73 – 20 and 76 – 20 and record.
T: Compare 73 – 20 to 73 – 2. Talk to your partner.
S: (Compare as previously.)
Repeat the process using the following sequence: 56 – 30, 56 – 3, 65 + 30, 35 + 60, 35 – 20, 35 – 30, 35 + 2,
32 + 5, 37 – 5, 87 – 5, 87 – 50. After each problem, ask students to share the easier problem that helped
them solve. Ask students to identify if they are adding or subtracting tens or ones.
Note: This Application Problem follows the Concept Development to allow students to apply their
understanding to a take from result unknown problem. The allotted time period includes 5 minutes to solve
the Application Problem and 10 minutes to complete the Problem Set.
The teacher has 48 folders. She gives 6 folders to the first table. How many folders does she have now?
NOTES ON
MULTIPLE MEANS
OF REPRESENTATION:
Rather than suggesting a strategy,
choose to share two different solution
strategies from students. Notice that
the drawings represent student work
at varying levels of sophistication.
When sharing, encourage students to
make connections between the
models.
MP.7
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Lesson 3 2 1
Note: This is the first application problem of Grade 2. The goal is to encourage all students to draw and solve
using the RDW process. Some students may simply know the answer, so it is important to establish the
purpose of the Application Problem of each lesson. It is the time to focus on understanding the situation
presented in the problem and representing that situation with a drawing, a number sentence, and a
statement of the answer. It is also the time for students to share their representations and their ways of
thinking, which can help more students access problem-solving strategies. Save the tape diagram from this
Application Problem to compare it to the tape diagram from Lesson 4 where students combine the parts
rather than subtract a part.
Problem Set (10 minutes)
Students should do their personal best to complete the Problem Set within the allotted 10 minutes. Some
problems do not specify a method for solving. Students should solve these problems using the RDW
approach used for Application Problems.
For some classes, it may be appropriate to modify the assignment by specifying which problems students
should work on first. With this option, let the purposeful sequencing of the Problem Set guide your selections
so that problems continue to be scaffolded. Balance word problems with other problem types to ensure a
range of practice. Consider assigning incomplete problems for homework or at another time during the day.
Lesson Objective: Add and subtract like units.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner before going over answers as a class. Look for
misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the
lesson.
Any combination of the questions below may be used to
lead the discussion.
What is another problem that could be added to
Problem 1(a)?
Compare 24 + 5 to 24 + 50 with your partner.
What’s different?
Share your explanation from Problem 4. What is another pair of addition sentences that has this
same relationship?
Do you think you could teach what you learned to someone else? How?
Can you figure out the math goal of today’s lesson? What name would you give this lesson?
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Lesson 3 2 1
After the Student Debrief, instruct students to complete
the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that
were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read
aloud to the students.
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Name Date
*Write the missing number. Pay attention to the + and – signs.
1. 3 + 1 = __ 16. 6 + 2 = __
2. 13 + 1 = __ 17. 56 + 2 = __
3. 23 + 1 = __ 18. 7 + 2 = __
4. 1 + 2 = __ 19. 67 + 2 = __
5. 11 + 2 = __ 20. 87 + 2 = __
6. 21 + 2 = __ 21. 7 – 2 = __
7. 31 + 2 = __ 22. 47 – 2 = __
8. 61 + 2 = __ 23. 67 – 2 = __
9. 4 – 1 = __ 24. 26 + 3 = __
10. 14 – 1 = __ 25. 56 + __ = 59
11. 24 – 1 = __ 26. __ + 3 = 76
12. 54 – 1 = __ 27. 57 – __ = 54
13. 5 – 3 = __ 28. 77 – __ = 74
14. 15 – 3 = __ 29. __ – 4 = 73
15. 25 – 3 = __ 30. __ – 4 = 93
Number Correct:
A
Lesson 3 Sprint 2 1
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Name Date
*Write the missing number. Pay attention to the + and – signs.
1. 2 + 1 = __ 16. 7 + 2 = __
2. 12 + 1 = __ 17. 67 + 2 = __
3. 22 + 1 = __ 18. 4 + 5 = __
4. 3 + 2 = __ 19. 54 + 5 = __
5. 13 + 2 = __ 20. 84 + 5 = __
6. 23 + 2 = __ 21. 8 – 6 = __
7. 43 + 2 = __ 22. 48 – 6 = __
8.. 63 + 2 = __ 23. 78 – 6 = __
9. 5 – 1 = __ 24. 33 + 4 = __
10. 15 – 1 = __ 25. 63 + __ = 67
11. 25 – 1 = __ 26. __ + 3 = 77
12. 45 – 1 = __ 27. 59 – __ = 56
13. 5 – 4 = __ 28. 79 – __ = 76
14. 15 – 4 = __ 29. __ – 6 = 73
15. 25 – 4 = __ 30. __ – 6 = 93
Number Correct:
B
Lesson 3 Sprint 2 1
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Lesson 3 Problem Set 2 1
Name Date
1. Solve.
a. 30 + 6 = _____
30 + 60 = _____
35 + 40 = _____
35 + 4 = _____
b. 50 – 30 = _____
51 – 30 = _____
57 – 4 = _____
57 – 40 = _____
2. Solve.
a. 24 + 5 = _____ b. 24 + 50 = _____
c. 78 – 3 = _____ d. 78 – 30 = _____
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3. Solve.
a. 38 + 10 = _____
18 + 30 = _____
b. 35 – 10 = _____
35 – 20 = _____
c. 56 + 40 = _____
46 + 50 = _____
d. 75 – 40 = _____
75 – 30 = _____
4. Compare 57 – 2 to 57 – 20. How are they different? Use words, drawings, or
numbers to explain.
Extension!
5. Andy had $28. He spent $5 on a book.
Lisa had $20 and got $3 more.
Lisa says she has more money.
Prove her right or wrong using pictures, numbers, or words.
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Name Date
Solve.
1. 23 + 5 = _____ 2. 68 – 5 = _____
3. 43 + 30 = _____ 4. 76 – 60 = _____
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Name Date
1. Solve.
a. 20 + 7 = _____
20 + 70 = _____
62 + 3 = _____
62 + 30 = _____
b. 80 – 20 = _____
85 – 2 = _____
85 – 20 = _____
86 – 20 = _____
c. 30 + 40 = _____
31 + 40 = _____
35 + 4 = _____
45 + 30 = _____
d. 70 – 30 = _____
75 – 30 = _____
78 – 3 = _____
75 – 40 = _____
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2. Solve.
a. 42 + 7 = _____ b. 24 + 70 = _____
c. 49 – 2 = _____ d. 98 – 20 = _____
3. Solve.
a. 16 + 3 = _____
13 + 6 = _____
b. 37 – 3 = _____
37 – 4 = _____
c. 26 + 70 = _____
76 + 20 = _____
d. 97 – 50 = _____
97 – 40 = _____
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Lesson 4 2
Lesson 4
Objective: Make a ten to add within 20.
Draw Tens and Ones 2.OA.2 (3 minutes)
Make Ten 2.OA.2 (3 minutes)
Make the Next Ten Within 100 2.OA.2 (4 minutes)
Take Out One 2.OA.2 (2 minutes)
Draw Tens and Ones (3 minutes)
Materials: (T) Linking cubes with ten-sticks and extra cubes, place value chart (S) Personal white
board
Note: This fluency activity reviews place value as students analyze two representations of
two-digit numbers.
T: Draw the number of cubes I show with quick tens and ones.
T: (Show 2 linking cube ten-sticks and 4 ones.)
S: (Draw as pictured to the right.)
T: Show me your boards. Tell me the number.
S: 24.
T: Draw the number I show with quick tens and ones.
T: (Write the number 42 on the place value chart.)
S: (Draw as pictured to the right.)
T: Tell me the number.
S: 42.
For the next minute, represent 18 and 81, 37 and 73, 29 and 92, alternating between showing the smaller
number of each pair with cubes and the larger number with the place value chart.
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Lesson 4 2
NOTES ON
MULTIPLE MEANS
OF REPRESENTATION:
Once the Rekenrek is removed,
encourage students who need support
to visualize the beads (ten-frames or 5-
groups), or guide them to use fingers to
model the number of ones in order to
determine how many more make ten.
Make Ten (3 minutes)
Note: This is a foundational skill for mastery of sums and differences to 20.
T: I’ll say a number, and you say how many more to make ten.
T: 9. Get ready.
S: 1.
T: Write the addition sentence. (Pause.) Show me your boards.
S: (Show 9 + 1 = 10.)
T: (Scan each board, and accept 1 + 9 = 10, 10 = 9 + 1, etc.)
T: 8. (Pause as students write.) Get ready.
S: 2.
T: Write the addition sentence. (Pause.) Show me your boards.
S: (Show 8 + 2 = 10.)
Continue with the following possible sequence: 2, 5, 6, 4, 7, and 3.
Make the Next Ten Within 100 (4 minutes)
Materials: (T) Rekenrek (S) Personal white board
Note: In this fluency activity, students apply their knowledge of partners to ten to find analogous partners to
20, 30, and 40 to prepare for today’s lesson. Keep them motivated to use the patterns by removing the
Rekenrek at times.
T: (Show 19.) Say the number.
S: 19.
T: Write the number sentence, starting with 19, to get to
or make the next ten on your personal white board.
S: (Write 19 + 1 = 20.)
T: (Scan the boards.) Tell me the addition sentence.
S: 19 + 1 = 20.
T: (Move 1 bead to make 20 as students answer.)
S: 39.
T: Write the number sentence, starting with 39, to make the next ten on your personal white board.
S: (Write 39 + 1 = 40.)
T: (Scan the boards.) Tell me the addition sentence.
S: 39 + 1 = 40.
T: (Move 1 bead to make 40 as students answer.)
Continue with the following possible sequence: 15, 35, 85; 18, 48, 68; 12, 52, and 92.
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Lesson 4 2
NOTES ON
MULTIPLE MEANS
OF ENGAGEMENT:
If time or precision is a factor, create
templates of pre-drawn circles to
model addends of 9, 8, and 7. Then,
students can attend to drawing Xs to
complete the ten and model the
remainder of the problem.
Take Out One (2 minutes)
Note: In the lesson, students add 9 and 6 by adding 9 and 1 and 5. They “take out 1” from 5.
T: Let’s take out 1 from each number. I say 5. You write the number bond and say the
two parts, 1 and 4.
T: 5.
S: (Draw number bond.) 1 and 4.
Continue with the following possible sequence: 3, 10, 4, 7, 9, 8, and 6.
Mark had a stick of 9 green linking cubes. His friend gave him 4
yellow linking cubes. How many linking cubes does Mark have
now?
Note: This add to result unknown problem’s tape diagram can
be compared to that of Lesson 3 when a part was subtracted.
Part 1: Making ten from an addend of 9, 8, or 7.
Note: In Grade 1, students used ten-sticks and quick ten
drawings extensively when making ten. Now in Grade 2, the
objective is to work at the numerical level as soon as possible.
T: (Write 9 + 4 on the board.)
T: Let’s draw to solve 9 + 4 using circles and Xs.
NOTES ON
MULTIPLE MEANS
OF REPRESENTATION:
“Mark’s Linking Cubes” bridges into
today’s Concept Development of
making a ten to add. Rather than
teach the make ten strategy during the
Application Problem, notice what
strategies students are independently
using, and integrate these observations
into the Concept Development. During
the Student Debrief, consider coming
back to the Application Problem, and
invite students to apply today’s
learning to show another way to solve
the problem.
MP.2
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Lesson 4 2
T: (Quickly draw and count aloud 9 circles in a 5-group column as seen in the first
image.)
T: How many Xs will we add?
S: 4 Xs.
T: (Using the X symbol, complete the ten and draw the other 3 Xs to the right as
seen in the second image.)
T: Did we make a ten?
S: Yes!
T: Our 9 + 4 is now a ten-plus fact. What fact can you see in the drawing?
S: 10 + 3 = 13.
T: 10 + 3 equals?
S: 13.
T: So, 9 + 4 equals?
S: 13. (Write the solution.)
T: What did we take out of 4 so that we could make 10?
S: 1.
T: (Draw the number bond under 4 as shown to the right.)
T: (Write 9 + 5.)
T: Solve using a number bond. (If students want or need to draw, allow them to.)
Continue with the following possible sequence: 9 + 6, 9 + 7, 8 + 9, 8 + 3, 8 + 4, 8 + 7, and 7 + 5. Have students
explain their work to a partner.
Part 2: Observing patterns.
T: Look at our list of problems where one part, or addend, is 9. Tell your partner what you notice
about adding to 9.
S: You get 1 out! The answer is 10 and 1 less than the other addend.
T: Look at the problems with 8 as an addend. Tell your partner what you notice.
S: You get 2 out! You always take 2 out of the other addend.
T: How is solving 9 + 4 and 8 + 4 different?
S: We used 2 to make 10 when we added to 8 and 1 to make 10 when we added to 9. We used a
different number bond.
Problem Set (10 minutes)
Students should do their personal best to complete the Problem Set within the allotted 10 minutes. Some
problems do not specify a method for solving. This is an intentional reduction of scaffolding that invokes
MP.5, Use Appropriate Tools Strategically. Students should solve these problems using the RDW approach
used for Application Problems.
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Lesson 4 2
Lesson Objective: Make a ten to add within 20.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner before going over answers as a class. Look for
misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the
lesson.
Any combination of the questions below may be used to
lead the discussion.
Let’s look at Problems 11–14. How are the
problems the same and different?
Do you notice a pattern that will help you
memorize your 9-plus facts? What other
patterns do you notice?
Explain the strategy we reviewed today. Can you
think of another problem that the make ten
strategy will help us solve?
Can you figure out the math goal of today’s
lesson? What name would you give this lesson?
After the Student Debrief, instruct students to complete
the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that
were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read
aloud to the students.
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Name Date
Solve.
1. 9 + 3 = ____ 2. 9 + 5 = ____
3. 8 + 4 = _____ 4. 8 + 7 = _____
5. 7 + 5 = _____ 6. 7 + 6 = _____
7. 8 + 8 = _____ 8. 9 + 8 = _____
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Solve.
13. Lisa has 2 blue beads and 9 purple beads. How many beads does Lisa have in all?
Lisa has _____ beads in all.
_________________________________________________________________
14. Ben had 8 pencils and bought 5 more. How many pencils does Ben have altogether?
_______________________________
9.
10 + ____ = 12
9 + ____ = 12
10.
10 + ____ = 13
9 + ____ = 13
11.
10 + ____ = 14
8 + ____ = 14
12.
10 + ____ = 16
7 + ____ = 16
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Name Date
Solve.
1. 9 + 6 = ____ 2. 8 + 5 = ____
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Name Date
Solve.
1. 8 + 4 = ____
/
2 2
8 + 2 = 10
10 + 2 = 12
2. 9 + 7 = ____
3. 9 + 3 = _____ 4. 8 + 6 = _____
5. 7 + 6 = _____ 6. 7 + 8 = _____
7. 8 + 8 = _____ 8. 8 + 9 = _____
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9. Solve and match.
10. Ronnie uses 5 brown bricks and 8 red bricks to build a fort.
How many bricks does Ronnie use in all?
Ronnie uses _____ bricks.
B
9 + 8 = ____
9 + 6 = ____
7 + 6 = ____
6 + 8 = ____
3 + 9 = ____
A
10 + ____ = 12
10 + ____ = 13
10 + ____ = 17
10 + ____ = 15
4 + ____ = 14
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Lesson 5 2
NOTES ON
MULTIPLE MEANS
OF ACTION AND
EXPRESSION:
If students need more support to
understand two-digit numbers as tens
and ones, use the Hide Zero cards as
used in Lesson 2.
Partner A models the tens; Partner B,
the ones. Pairs move together and
overlap the cards to model the number
(e.g., 24). Likewise, they move apart
for the break apart portion, separating
the cards to model the value of the
tens and ones (e.g., 20 and 4).
Lesson 5
Objective: Make a ten to add within 100.
Happy Counting: Say Ten Way 2.OA.2 (2 minutes)
Put Together/Take Apart 2.OA.2 (3 minutes)
Make the Next Ten Within 100 2.OA.2 (5 minutes)
Happy Counting: Say Ten Way (2 minutes)
Note: Continued work with counting the Say Ten Way gives
students confidence and allows them to build proficiency.
T: Let’s Happy Count the Say Ten Way. Let’s start at 6
tens 2. Ready?
S: 6 tens 2, 6 tens 1, 6 tens, 5 tens 9, 6 tens, 6 tens 1, 6
tens, 5 tens 9, 5 tens 8, 5 tens 9, 6 tens.
T: Excellent! Try it for 30 seconds with your partner.
Partner B, you are the teacher today.
Put Together/Take Apart (3 minutes)
Note: Students remember the relevance of ten-plus facts to larger numbers.
Put Together
T: When I say a ten-plus fact, you say the answer on my
signal.
T: 10 + 5. (Signal.)
S: 15.
T: 10 + 2.
S: 12.
Continue with the following possible sequence: 10 + 9, 20 + 1, 20 + 4, 50 + 4, 80 + 4, 30 + 8, 40 + 8, 70 + 8,
90 + 8.
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Lesson 5 2
Take Apart
T: Now, when I say 13, you say 10 + 3.
T: 13. (Signal.)
S: 10 + 3.
Continue with the following possible sequence: 17, 11, 16, 18, 28, 78, 14, 34, and 94.
Make the Next Ten Within 100 (5 minutes)
Materials: (T) Rekenrek (S) Personal white board
Note: In this fluency activity, students apply their knowledge of partners to ten to find analogous partners to
20, 30, and 40, which prepares them for today’s lesson.
For 30 seconds, say numbers 0–10. Students say partners to ten at the signal. Then, remove the Rekenrek.
S: 9.
T: Tell me the number sentence to make ten.
S: 9 + 1 = 10.
T: (Move 1 bead to make 10. Show 19.)
T: Say the number.
S: 19.
T: Write the number sentence to make 20.
S: 19 + 1 = 20.
Continue with the following possible sequence: 29, 39; 5, 15, 25, 35; 8, 18, 28, 38; 7, 17, 27, and 37.
T: (Write 39 + 4.) Talk to your partner about how you would solve this problem.
S: We can draw 39 circles and 4 Xs and count them all. I can count on starting at 39. 40, 41, 42, 43.
You can add 1 to make 40 and add the 3. 40 + 3 = 43.
T: Draw 39 using quick tens and circles.
S: (Draw.)
T: Show me your board! (Pause. Ask students to
redraw to show 9 either as a 5-group column or
in a ten-frame configuration.)
T: Now draw 4 Xs. (Quietly remind certain
students to complete the ten first.)
T: Write the number sentence with the solution.
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Lesson 5 2
NOTES ON
MULTIPLE MEANS
OF ENGAGEMENT:
Scaffold questioning to guide
connections, as in 49 + 5:
How many more does 9 need to
make a 10? How about 19? 29?
Where can we get 1 more?
What should we take out of the
other addend?
How does your number bond
match your quick ten drawing?
T: 39 + 4 equals?
S: 43.
T: 39 + 4 equals 40 plus …?
S: 3.
T: (Write 39 + 4 = 40 + 3.)
T: Let’s show 39 + 4 using a number bond. We started
with 39. How did we break apart 4 so we can make
40?
S: 1 and 3. (Write number bond as shown in the image
on the previous page.)
Repeat the process with the following suggested sequence:
49 + 5, 79 + 5, 48 + 5, 78 + 5, 7 + 29, 7 + 48, and 77 + 6. Students
should demonstrate understanding using at least one
representation such as quick tens and ones or number bonds.
Mia counted all the fish in a tank. She counted 38 goldfish and 4 black fish. How many fish were in the tank?
Note: If students do not use the tape diagram, model it after two students have shared their solution
strategies. Be sure to make connections between the different representations in students’ drawings.
“What part of the drawing using the ten-frames represents the goldfish?” “What part of the tape diagram
represents the goldfish?” “Which drawing is more efficient?”
This Application Problem follows the Concept Development to provide an opportunity for students to apply
the make ten strategy in the context of a put together total unknown problem. The allotted time period
includes 8 minutes to solve the Application Problem and 10 minutes to complete the Problem Set.
NOTES ON
APPLICATION
PROBLEMS:
These are the four steps of the
problem-solving process:
1. Read.
2. Draw.
3. Write a number sentence.
4. Write a word sentence.
This process provides accommodation
for students with disabilities and
English language learners since it is
both visual and kinesthetic.
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ACFrOgCUndx2gwZatyTMzxmPUupu5d_2sckQSqN9-E0_zASUZLVnHEnWwdepNxwkHzWB-cIgvYsw7EN2lUX0Ta83BGPUyAg9H_aKAk-fAlhXm9vZrHcyxPE5SeklkdFdr6KbaCSys4uxy7Nt4KnY.pdf

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